Question

Find the radius of a circle whose area is equal to the difference of the areas of two circles of radii 6 cm and 10 cm respectively​

Answer 1

Step-by-step explanation:

phi R^2=phi r1^2+phi r2^2. phi R^2=phi(8^2+6^2). R=10. therefore the radius of the third circle of 10.CM

Answer 2

$\sf\small\underbrace\red{Given} \\ \tt{\implies Radius\:of \: {two\:circle}=6cm\:and\:10cm} \\ \\ \sf\small\underbrace\red{To\:Find}\\ \tt{\implies The\:radius\:of \: {new\:circle}} \\ \\ \sf\small\underbrace\red{Solution} \\ \sf\small\blue{Formula\:used:-}\\ \boxed{ \pmb { Area\:of\:circle=\pi\:r^2} }\\ \\ \bf{ Difference\:_{(area\:of\:2\: cicle)}=Area\:_{(new\:circle)}} \\ \rm{ \pi\:(r^1)^2-\pi\:(r^2)^2=\pi\:r^2} \\ \rm{ \pi\:(10)^2-\pi\:(6)^2=\pi\:r^2} \\ \rm{ \pi(10^2-6^2)=\pi\:r^2} \\ \rm{ \pi(100-36)=\pi\:r^2} \\ \rm{ \pi(64)=\pi\:r^2} \\ \tt{ r^2=64} \\ \rm{ r=\sqrt{64}} \\ \tt{ r=8cm} \\ \rm{ The\:radius\:of \: {new\:circle}=8cm}</p><p></p><p>$